{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np \n",
    "import torch\n",
    "import math\n",
    "import d2lzh as d2l\n",
    "import matplotlib.pyplot as plt "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "epoch 10,x: 0.06046617599999997\n"
    },
    {
     "output_type": "display_data",
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "def gd(eta):\n",
    "    x = 10\n",
    "    results = [x]\n",
    "    for i in range(10):\n",
    "        x -= eta * 2 * x \n",
    "        results.append(x)\n",
    "    print(\"epoch 10,x:\",x)\n",
    "    return results\n",
    "\n",
    "res = gd(0.2)\n",
    "\n",
    "def show_trace(res):\n",
    "    n = max(abs(min(res)),abs(max(res)),10)\n",
    "    f_line = np.arange(-n,n,0.1)\n",
    "    plt.plot(f_line,[x * x for x in f_line])\n",
    "    plt.plot(res,[x * x for x in res],\"-o\")\n",
    "    plt.xlabel(\"x\")\n",
    "    plt.ylabel(\"f(x)\")\n",
    "\n",
    "show_trace(res)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "epoch 10,x: 3.4867844009999995\n"
    },
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "# 学习速率 0.05\n",
    "show_trace(gd(0.05))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "epoch 10,x: 61.917364224000096\n"
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "# 过大的学习速率1.1\n",
    "show_trace(gd(1.1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 多维度梯度下降"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "epoch 20,x1 -0.057646,x2 -0.000073\n"
    },
    {
     "output_type": "display_data",
     "data": {
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "def train_2d(trainer):\n",
    "    x1,x2,s1,s2 = -5,-2,0,0\n",
    "    results = [(x1,x2)]\n",
    "    for i in range(20):\n",
    "        x1,x2,s1,s2 = trainer(x1,x2,s1,s2)\n",
    "        results.append((x1,x2))\n",
    "\n",
    "    print(\"epoch %d,x1 %f,x2 %f\" %(i +1 ,x1,x2))\n",
    "    return results\n",
    "\n",
    "def show_trace_2d(f,results):\n",
    "    plt.plot(*zip(*results),\"-o\",color=\"#ff7f0e\")\n",
    "    x1,x2 = np.meshgrid(np.arange(-5.5,1.0,0.1),np.arange(-3.0,1.0,0.1))\n",
    "    plt.contour(x1,x2,f(x1,x2),colors=\"#1f77b4\")\n",
    "    plt.xlabel(\"x1\")\n",
    "    plt.ylabel(\"x2\")\n",
    "\n",
    "eta=0.1\n",
    "\n",
    "def f_2d(x1,x2):\n",
    "    return x1 ** 2 + 2 * x2 ** 2\n",
    "\n",
    "def gd_2d(x1,x2,s1,s2):\n",
    "    return (x1-eta * 2 * x1,x2 -eta * 4 * x2,0,0)\n",
    "\n",
    "show_trace_2d(f_2d,train_2d(gd_2d))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "epoch 20,x1 -0.160970,x2 -0.221283\n"
    },
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "def sgd_2d(x1,x2,s1,s2):\n",
    "    return (x1 - eta *(2 * x1 + np.random.normal(0.1)),\n",
    "    x2 - eta * (4 * x2 + np.random.normal(0.1)),0,0)\n",
    "\n",
    "show_trace_2d(f_2d,train_2d(sgd_2d))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 7.3　小批量随机梯度下降"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "torch.Size([1500, 5])"
     },
     "metadata": {},
     "execution_count": 7
    }
   ],
   "source": [
    "import numpy as np \n",
    "import matplotlib.pyplot as plt \n",
    "import time\n",
    "import torch\n",
    "import torch.nn as nn \n",
    "import d2lzh as d2l \n",
    "\n",
    "def get_data_ch7():\n",
    "    data = np.genfromtxt(\"../data/airfoil_self_noise.data\",delimiter=\"\\t\")\n",
    "    data = (data - data.mean(axis=0)) / data.std(axis=0)\n",
    "    return torch.tensor(data[:1500,:-1],dtype=torch.float32),torch.tensor(data[:1500,-1],dtype=torch.float32)\n",
    "\n",
    "feature,labels = get_data_ch7()\n",
    "feature.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "loss: 0.243531, 0.039447 sec per epoch \n"
    },
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "def sgd(params,states,hyperparams):\n",
    "    for p in params:\n",
    "        p.data -= hyperparams[\"lr\"] *p.grad.data\n",
    "\n",
    "def train_ch7(optimizer_fn,states,hyperparams,features,labels,batch_size=10,num_epochs=2):\n",
    "    net,loss = d2l.linreg,d2l.squared_loss\n",
    "\n",
    "    w = torch.nn.Parameter(torch.tensor(np.random.normal(0,0.01,size=(features.shape[1],1)),dtype=torch.float32),requires_grad=True)\n",
    "    b = torch.nn.Parameter(torch.zeros(1,dtype=torch.float32),requires_grad=True)\n",
    "\n",
    "    def eval_loss():\n",
    "        return loss(net(features,w,b),labels).mean().item()\n",
    "\n",
    "    ls = [eval_loss()]\n",
    "    data_iter = torch.utils.data.DataLoader(torch.utils.data.TensorDataset(features,labels),batch_size,shuffle=True)\n",
    "\n",
    "    for _ in range(num_epochs):\n",
    "        start = time.time()\n",
    "        for batch_i,(x,y) in enumerate(data_iter):\n",
    "            l = loss(net(x,w,b),y).mean()\n",
    "\n",
    "            if w.grad is not None:\n",
    "                w.grad.data.zero_()\n",
    "                b.grad.data.zero_()\n",
    "\n",
    "            l.backward()\n",
    "            optimizer_fn([w,b],states,hyperparams)\n",
    "            if(batch_i + 1) * batch_size % 100 == 0:\n",
    "                ls.append(eval_loss())\n",
    "\n",
    "    print(\"loss: %f, %f sec per epoch \"%(ls[-1],time.time()-start))\n",
    "    plt.plot(np.linspace(0,num_epochs,len(ls)),ls)\n",
    "    plt.xlabel(\"epoch\")\n",
    "    plt.ylabel(\"loss\")\n",
    "\n",
    "def train_sgd(lr,batch_size,num_epochs=2):\n",
    "    train_ch7(sgd,None,{\"lr\":lr},feature,labels,batch_size,num_epochs)\n",
    "\n",
    "train_sgd(1,1500,6)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "loss: 0.246039, 0.290179 sec per epoch \n"
    },
    {
     "output_type": "display_data",
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "train_sgd(0.005,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "loss: 0.244371, 0.042735 sec per epoch \n"
    },
    {
     "output_type": "display_data",
     "data": {
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "train_sgd(0.05,10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "batch较大，则一个训练周期内，迭代次数较少，每个训练周期的时间较短，就需要增大epoch；batch较小，一个训练周期内，迭代次数较多，每个训练周期的时间较长，可以减小epoch."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def train_pytorch_ch7(optimizer_fn,optimizer_hyperparams,features,labels,batch_size=10,num_epochs=2):\n",
    "\n",
    "    net = nn.Sequential(\n",
    "        nn.Linear(features.shape[-1],1)\n",
    "    )\n",
    "    loss = nn.MSELoss()\n",
    "\n",
    "    optimizer = optimizer_fn(net.parameters(),**optimizer_hyperparams)\n",
    "\n",
    "    def eval_loss():\n",
    "        return loss(net(features).view(-1),labels).item() / 2\n",
    "\n",
    "    ls = [eval_loss()]\n",
    "    data_iter = torch.utils.data.DataLoader(torch.utils.data.TensorDataset(features,labels),batch_size,shuffle=True)\n",
    "\n",
    "    for _ in range(num_epochs):\n",
    "        start = time.time()\n",
    "\n",
    "        for batch_i,(x,y) in enumerate(data_iter):\n",
    "            l = loss(net(x).view(-1),y) / 2\n",
    "\n",
    "            optimizer.zero_grad()\n",
    "            l.backward()\n",
    "            optimizer.step()\n",
    "            if(batch_i + 1) * batch_size % 100 == 0:\n",
    "                ls.append(eval_loss())\n",
    "\n",
    "    print(\"loss: %f, %f sec per epoch \"%(ls[-1],time.time()-start))\n",
    "    plt.plot(np.linspace(0,num_epochs,len(ls)),ls)\n",
    "    plt.xlabel(\"epoch\")\n",
    "    plt.ylabel(\"loss\") "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "loss: 0.244184, 0.032329 sec per epoch \n"
    },
    {
     "output_type": "display_data",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "train_pytorch_ch7(torch.optim.SGD,{\"lr\":0.05},feature,labels,10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
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